Search results for "Variable"
showing 10 items of 1674 documents
Recursive estimation of the conditional geometric median in Hilbert spaces
2012
International audience; A recursive estimator of the conditional geometric median in Hilbert spaces is studied. It is based on a stochastic gradient algorithm whose aim is to minimize a weighted L1 criterion and is consequently well adapted for robust online estimation. The weights are controlled by a kernel function and an associated bandwidth. Almost sure convergence and L2 rates of convergence are proved under general conditions on the conditional distribution as well as the sequence of descent steps of the algorithm and the sequence of bandwidths. Asymptotic normality is also proved for the averaged version of the algorithm with an optimal rate of convergence. A simulation study confirm…
Pairwise Markov properties for regression graphs
2016
With a sequence of regressions, one may generate joint probability distributions. One starts with a joint, marginal distribution of context variables having possibly a concentration graph structure and continues with an ordered sequence of conditional distributions, named regressions in joint responses. The involved random variables may be discrete, continuous or of both types. Such a generating process specifies for each response a conditioning set that contains just its regressor variables, and it leads to at least one valid ordering of all nodes in the corresponding regression graph that has three types of edge: one for undirected dependences among context variables, another for undirect…
Elasticity function of a discrete random variable and its properties
2017
ABSTRACTElasticity (or elasticity function) is a new concept that allows us to characterize the probability distribution of any random variable in the same way as characteristic functions and hazard and reverse hazard functions do. Initially defined for continuous variables, it was necessary to extend the definition of elasticity and study its properties in the case of discrete variables. A first attempt to define discrete elasticity is seen in Veres-Ferrer and Pavia (2014a). This paper develops this definition and makes a comparative study of its properties, relating them to the properties shown by discrete hazard and reverse hazard, as both defined in Chechile (2011). Similar to continuou…
Criteria for Bayesian model choice with application to variable selection
2012
In objective Bayesian model selection, no single criterion has emerged as dominant in defining objective prior distributions. Indeed, many criteria have been separately proposed and utilized to propose differing prior choices. We first formalize the most general and compelling of the various criteria that have been suggested, together with a new criterion. We then illustrate the potential of these criteria in determining objective model selection priors by considering their application to the problem of variable selection in normal linear models. This results in a new model selection objective prior with a number of compelling properties.
Optimal Reporting of Predictions
1989
Abstract Consider a problem in which you and a group of other experts must report your individual predictive distributions for an observable random variable X to some decision maker. Suppose that the report of each expert is assigned a prior weight by the decision maker and that these weights are then updated based on the observed value of X. In this situation you will try to maximize your updated, or posterior, weight by appropriately choosing the distribution that you report, rather than necessarily simply reporting your honest predictive distribution. We study optimal reporting strategies under various conditions regarding your knowledge and beliefs about X and the reports of the other e…
Testing equality of reliability and stability with simple linear constraints in multi-wave, multi-variable models
1998
Data from a longitudinal study on school achievement were used to develop new methods for analysing reliability of measurements and stability of behaviour over a long time interval. The proposed method of analysis makes it possible to test hypotheses about equality constraints on reliability and stability. It is known that the use of negative variances for imaginary latent variables with equality constraints between structural parameters produces standardized variances for endogenous latent variables and quality constraints for coefficients of stability. Reparameterization of random errors in measurement models allows equality constraints to be set for coefficients of cross-sectional and of…
Central Limit Theorem for Linear Eigenvalue Statistics for a Tensor Product Version of Sample Covariance Matrices
2017
For $$k,m,n\in {\mathbb {N}}$$ , we consider $$n^k\times n^k$$ random matrices of the form $$\begin{aligned} {\mathcal {M}}_{n,m,k}({\mathbf {y}})=\sum _{\alpha =1}^m\tau _\alpha {Y_\alpha }Y_\alpha ^T,\quad {Y}_\alpha ={\mathbf {y}}_\alpha ^{(1)}\otimes \cdots \otimes {\mathbf {y}}_\alpha ^{(k)}, \end{aligned}$$ where $$\tau _{\alpha }$$ , $$\alpha \in [m]$$ , are real numbers and $${\mathbf {y}}_\alpha ^{(j)}$$ , $$\alpha \in [m]$$ , $$j\in [k]$$ , are i.i.d. copies of a normalized isotropic random vector $${\mathbf {y}}\in {\mathbb {R}}^n$$ . For every fixed $$k\ge 1$$ , if the Normalized Counting Measures of $$\{\tau _{\alpha }\}_{\alpha }$$ converge weakly as $$m,n\rightarrow \infty $$…
Fractional calculus approach to the statistical characterization of random variables and vectors
2009
Fractional moments have been investigated by many authors to represent the density of univariate and bivariate random variables in different contexts. Fractional moments are indeed important when the density of the random variable has inverse power-law tails and, consequently, it lacks integer order moments. In this paper, starting from the Mellin transform of the characteristic function and by fractional calculus method we present a new perspective on the statistics of random variables. Introducing the class of complex moments, that include both integer and fractional moments, we show that every random variable can be represented within this approach, even if its integer moments diverge. A…
Comparison between splines and fractional polynomials for multivariable model building with continuous covariates: a simulation study with continuous…
2012
In observational studies, many continuous or categorical covariates may be related to an outcome. Various spline-based procedures or the multivariable fractional polynomial (MFP) procedure can be used to identify important variables and functional forms for continuous covariates. This is the main aim of an explanatory model, as opposed to a model only for prediction. The type of analysis often guides the complexity of the final model. Spline-based procedures and MFP have tuning parameters for choosing the required complexity. To compare model selection approaches, we perform a simulation study in the linear regression context based on a data structure intended to reflect realistic biomedica…
On stability issues in deriving multivariable regression models
2014
In many areas of science where empirical data are analyzed, a task is often to identify important variables with influence on an outcome. Most often this is done by using a variable selection strategy in the context of a multivariable regression model. Using a study on ozone effects in children (n = 496, 24 covariates), we will discuss aspects relevant for deriving a suitable model. With an emphasis on model stability, we will explore and illustrate differences between predictive models and explanatory models, the key role of stopping criteria, and the value of bootstrap resampling (with and without replacement). Bootstrap resampling will be used to assess variable selection stability, to d…